Intro

Template for model comparisons:

The above diagram captures all 4 possible models combinations. The black is the univariate ALT model, and the blue adds all paths we estimate for the bivariate ALT. Red paths show the paths constrained to be 0 in the mean-only (fixed slope) model. Letter labels indicate paths constrained to be equal.

What are the best models that converge?

In the below figures, each bar represents the ‘model score’ of a model combination for a bivariate ALT model. A score of 2 indicates that there were no problems, 1 indicates that there were warnings about the standard error being computed (e.g., with MLF instead of MLR), and 0 indicates that there were errors (non-convergence).

The tables show the winning model giving preference to the full bivariate random slope ALT model, even if it was estimated with MLF instead of MLR (this is not very common in the national sample, but more so in the college sample).

The model for the personality variable comes first, so ‘Lin_MeanOnly’ means ‘full linear ALT model for personality variable, fixed mean slope ALT model for value variable.’

National

pVar aspfin BFA_MT HRZ_COL HRZ_IND MVS_mc USI VRT_COL VRT_IND
BFA_AC Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_AP Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_CI Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_CO Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_EA Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_EE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_NV Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_NW Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_OI Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_OO Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_A6 Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_C Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_E Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
bfi_hp8 Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_N Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_O Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
D_SCALE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
I_A Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
I_C Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
I_D Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
I_E Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
I_N Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
I_O Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
I_S Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
S_SCALE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
National Sample

National Sample

College

pVar aspfin BFA_MT HRZ_COL HRZ_IND MVS_mc USI VRT_COL VRT_IND
BFA_AC Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_AP Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_CI Lin_Lin Lin_Lin Lin_Lin Lin_Lin MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_CO Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin
BFA_EA Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_EE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_NV Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_NW Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_OI Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
BFA_OO Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_A6 Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_C Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
BFI_E Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly Lin_Lin Lin_Lin Lin_Lin
bfi_hp8 Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
BFI_N Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin
BFI_O Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
D_SCALE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_Lin
S_SCALE Lin_Lin Lin_Lin Lin_Lin Lin_Lin Lin_MeanOnly MeanOnly_Lin Lin_Lin Lin_Lin Lin_Lin
College Sample

College Sample

Non-Lin_Lin Models: Univariate best-fit

sample pVar vVar bestCombo AIC_P BIC_P LL_P AIC_V BIC_V LL_V
Col BFA_CI MVS_mc MeanOnly_Lin AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFA_CO VRT_IND Lin_MeanOnly MeanOnly_Lin AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFA_EE MVS_mc Lin_MeanOnly MeanOnly_Lin AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFA_NW MVS_mc Lin_MeanOnly MeanOnly_Lin AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFA_OI MVS_mc Lin_MeanOnly MeanOnly_Lin AR_LinM AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFI_A6 MVS_mc Lin_MeanOnly MeanOnly_Lin AR_LinM AR_LinM AR_LinM AR_Int AR_Int AR_Int
Col BFI_C MVS_mc Lin_MeanOnly AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFI_E MVS_mc Lin_MeanOnly AR_LinM AR_Int AR_Int AR_Int AR_Int AR_Int
Col BFI_N VRT_IND Lin_MeanOnly MeanOnly_Lin AR_Int AR_Int AR_Int AR_Int AR_Int AR_Int
Col S_SCALE MVS_mc Lin_MeanOnly MeanOnly_Lin AR_Lin AR_Int AR_Int AR_Int AR_Int AR_Int
Nat I_C MVS_mc Lin_MeanOnly AR_LinM AR_LinM AR_LinM AR_Lin AR_Lin AR_Lin
Nat I_E MVS_mc Lin_MeanOnly AR_LinM AR_Int AR_LinM AR_Lin AR_Lin AR_Lin
Nat I_N MVS_mc Lin_MeanOnly AR_LinM AR_Int AR_LinM AR_Lin AR_Lin AR_Lin
Nat I_O MVS_mc Lin_MeanOnly AR_Int AR_Int AR_Int AR_Lin AR_Lin AR_Lin

Parameter plots

National: AR paths across variable combinations and model types

National: XL paths across variable combinations and model types

College: AR paths across variable combinations and model types

College: XL paths across variable combinations and model types

National: Within-wave correlations across variable combinations and model types

College: Within-wave correlations across variable combinations and model types